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Purpose Physicians utilize cerebral perfusion maps (e.g., cerebral blood flow, cerebral blood volume, transit time) to prescribe the plan of care for stroke patients. Variability in scanning techniques and post-processing software can result in differences between these perfusion maps. To determine which techniques are acceptable for clinical care, it is important to validate the accuracy and reproducibility of the perfusion maps. Validation using clinical data is challenging due to the lack of a gold standard to assess cerebral perfusion and the impracticality of scanning patients multiple times with different scanning techniques. In contrast, simulated data from a realistic digital phantom of the cerebral perfusion in acute stroke patients would enable studies to optimize and validate the scanning and post-processing techniques. Methods We describe a complete framework to simulate CT perfusion studies for stroke assessment. We begin by expanding the XCAT brain phantom to enable spatially varying contrast agent dynamics and incorporate a realistic model of the dynamics in the cerebral vasculature derived from first principles. A dynamic CT simulator utilizes the time-concentration curves to define the contrast agent concentration in the object at each time point and generates CT perfusion images compatible with commercially available post-processing software. We also generate ground truth perfusion maps to which the maps generated by post-processing software can be compared. Results We demonstrate a dynamic CT perfusion study of a simulated patient with an ischemic stroke and the resulting perfusion maps generated by post-processing software. We include a visual comparison between the computer-generated perfusion maps and the ground truth perfusion maps. The framework is highly tunable; users can modify the perfusion properties (e.g., occlusion location, CBF, CBV, and MTT), scanner specifications (e.g., focal spot size and detector configuration), scanning protocol (e.g., kVp and mAs), and reconstruction parameters (e.g., slice thickness and reconstruction filter). Conclusions This framework provides realistic test data with the underlying ground truth that enables a robust assessment of CT perfusion techniques and post-processing methods for stroke assessment.

Transcranial magnetic resonance-guided focused ultrasound (tcMRgFUS) is gaining significant acceptance as a noninvasive treatment for motion disorders and shows promise for novel applications such as blood-brain barrier opening for tumor treatment. A typical procedure relies on CT-derived acoustic property maps to simulate the transfer of ultrasound through the skull. Accurate estimates of the acoustic attenuation in the skull are essential to accurate simulations, but there is no consensus about how attenuation should be estimated from CT images and there is interest in exploring MR as a predictor of attenuation in the skull. In this study, we measure the acoustic attenuation at 0.5, 1, and 2.25 MHz in 89 samples taken from two ex vivo human skulls. CT scans acquired with a variety of X-ray energies, reconstruction kernels, and reconstruction algorithms, and MR images acquired with ultrashort and zero echo time sequences are used to estimate the average Hounsfield unit value, MR magnitude, and T2* value in each sample. The measurements are used to develop a model of attenuation as a function of frequency and each individual imaging parameter.

Photon counting x-ray detectors (PCDs) with spectral capabilities have the potential to revolutionize computed tomography (CT) for medical imaging. The ideal PCD provides accurate energy information for each incident x-ray, and at high spatial resolution. This information enables material-specific imaging, enhanced radiation dose efficiency, and improved spatial resolution in CT images. In practice, PCDs are affected by non-idealities, including limited energy resolution, pulse pileup, and cross talk due to charge sharing, K-fluorescence, and Compton scattering. In order to maximize their performance, PCDs must be carefully designed to reduce these effects and then later account for them during correction and post-acquisition steps. This review article examines algorithms for using PCDs in spectral CT applications, including how non-idealities impact image quality. Performance assessment metrics that account for spatial resolution and noise such as the detective quantum efficiency (DQE) can be used to compare different PCD designs, as well as compare PCDs with conventional energy integrating detectors (EIDs). These methods play an important role in enhancing spectral CT images and assessing the overall performance of PCDs.

The past decade has seen the increasing integration of magnetic resonance (MR) imaging into radiation therapy (RT). This growth can be contributed to multiple factors, including hardware and software advances that have allowed the acquisition of high-resolution volumetric data of RT patients in their treatment position (also known as MR simulation) and the development of methods to image and quantify tissue function and response to therapy. More recently, the advent of MR-guided radiation therapy (MRgRT) - achieved through the integration of MR imaging systems and linear accelerators - has further accelerated this trend. As MR imaging in RT techniques and technologies, such as MRgRT, gain regulatory approval worldwide, these systems will begin to propagate beyond tertiary care academic medical centers and into more community-based health systems and hospitals, creating new opportunities to provide advanced treatment options to a broader patient population. Accompanying these opportunities are unique challenges related to their adaptation, adoption, and use including modification of hardware and software to meet the unique and distinct demands of MR imaging in RT, the need for standardization of imaging techniques and protocols, education of the broader RT community (particularly in regards to MR safety) as well as the need to continue and support research, and development in this space. In response to this, an ad hoc committee of the American Association of Physicists in Medicine (AAPM) was formed to identify the unmet needs, roadblocks, and opportunities within this space. The purpose of this document is to report on the major findings and recommendations identified. Importantly, the provided recommendations represent the consensus opinions of the committee's membership, which were submitted in the committee's report to the AAPM Board of Directors. In addition, AAPM ad hoc committee reports differ from AAPM task group reports in that ad hoc committee reports are neither reviewed nor ultimately approved by the committee's parent groups, including at the council and executive committee level. Thus, the recommendations given in this summary should not be construed as being endorsed by or official recommendations from the AAPM.

As we arrive at the 50th anniversary of the first computed tomography (CT) scan of a live patient, we take this opportunity to revisit the history of early CT development. It is not an exaggeration to say that the invention of CT may represent the greatest revolution in medical imaging since the discovery of x-rays. We cover events over a period of about two decades that started with the realization that accurate cross-sectional soft-tissue detail is possible and could be a significant advance. We describe in some detail the development of the first CT system and then the rapid technical advances during the following years that included the entry of many companies into the field and the circumstances that led many of those entrants to exit the field. Rather than focusing on the specific technical details (which can be found elsewhere), we include stories and events in the hope that broader lessons can be learned. As the first x-ray-based digital imaging modality, CT brought into common use an exceptional tool that benefits countless patients every day. It also introduced dramatic changes to biomedical imaging as a field that continues to influence progress to this day.

Photon counting x-ray detectors (PCDs) with energy discrimination capabilities provide spectral information, can eliminate electronic and Swank noise, and image multiple contrast agents simultaneously with high resolution. However, with high flux on the detectors, pulse pileup leads to count loss and spectral distortion. Accurate description of the output count rate and spectrum behavior of a PCD is crucial to the development of further applications, e.g., material decomposition. In this work, a fully analytical model of the pulse pileup spectrum and count statistics for a nonparalyzable detector with nonzero pulse length is proposed, which accounts for seminonparalyzable behavior, i.e., retriggering of counts by pulses incident during the dead time. We use a triangle to approximate a realistic pulse shape and recursively compute the output spectrum of different pulse pileup orders. A count-rate and spectrum dependent expression of count statistics is further derived based on renewal theory. Our analytical model can then be used to predict material decomposition noise using the Cramer–Rao lower bound (CRLB). We compared our model predictions with Monte Carlo simulations. The results show that our model can accurately predict the count loss and spectral distortion resulting from pulse pileup and can be used in predicting material decomposition noise over a large range of count rates.

In x-ray computed tomography (CT), materials with different elemental compositions can have identical CT number values, depending on the mass density of each material and the energy of the detected x-ray beam. Differentiating and classifying different tissue types and contrast agents can thus be extremely challenging. In multienergy CT, one or more additional attenuation measurements are obtained at a second, third or more energy. This allows the differentiation of at least two materials. Commercial dual-energy CT systems (only two energy measurements) are now available either using sequential acquisitions of low- and high-tube potential scans, fast tube-potential switching, beam filtration combined with spiral scanning, dual-source, or dual-layer detector approaches. The use of energy-resolving, photon-counting detectors is now being evaluated on research systems. Irrespective of the technological approach to data acquisition, all commercial multienergy CT systems circa 2020 provide dual-energy data. Material decomposition algorithms are then used to identify specific materials according to their effective atomic number and/or to quantitate mass density. These algorithms are applied to either projection or image data. Since 2006, a number of clinical applications have been developed for commercial release, including those that automatically (a) remove the calcium signal from bony anatomy and/or calcified plaque; (b) create iodine concentration maps from contrast-enhanced CT data and/or quantify absolute iodine concentration; (c) create virtual non-contrast-enhanced images from contrast-enhanced scans; (d) identify perfused blood volume in lung parenchyma or the myocardium; and (e) characterize materials according to their elemental compositions, which can allow in vivo differentiation between uric acid and non-uric acid urinary stones or uric acid (gout) or non-uric acid (calcium pyrophosphate) deposits in articulating joints and surrounding tissues. In this report, the underlying physical principles of multienergy CT are reviewed and each of the current technical approaches are described. In addition, current and evolving clinical applications are introduced. Finally, the impact of multienergy CT technology on patient radiation dose is summarized.

Quantitative perfusion maps of cerebral blood flow, cerebral blood volume, and transit time generated using dynamic imaging data enable physicians to evaluate and prescribe the optimal plan of care for stroke patients. Validation is needed to increase the accuracy and reproducibility of this data, which can vary depending on the scanning technique and post-processing algorithm. In this work, we expand the XCAT brain phantom to incorporate a realistic model of the contrast agent dynamics in the cerebral vasculature and establish the ground truth to which the perfusion maps can be compared. For a specific stroke case, each tissue region's flow demand is calculated and used to determine the feeding flow in the upstream arteries and draining flow in the downstream veins. Using the flow values and a contrast agent injection curve, the model calculates the input and output concentration curves for each structure in the brain. The concentration curve within each structure is then calculated as the difference between the total amount of contrast agent that has entered and exited the structure up until that timepoint. A dynamic simulation framework utilizes the curves to define the contrast agent concentration within the phantom at each time point and generates simulated CT perfusion imaging data sets compatible with commercially available post-processing software. This development provides a realistic set of ground truth test data that enables quantitative validation and optimization of perfusion imaging and post-processing methods for stroke assessment.

We present a new concept of full-scale cone-beam computed tomography (CT) spectral imaging with simultaneous scatter correction capability using a spectral modulator and flying focal spot technology. The design of the spectral modulator and the utilization of flying focal spot are investigated, revealing the feasibility of using the flying focal spot to improve the spectral data sampling for a stationary modulator. Based on our analytical analysis, with the flying focal spot, the spectral projection ray misalignment can be reduced by a factor of more than 8. For modulator design, common materials such as Cu, ZnSe, Mo, Ag and Sn could be good candidates for better energy separation at a given attenuation of photon flux. A proof-of-concept study of a Catphan600 phantom and an anthropomorphic chest phantom was conducted on a tabletop cone-beam CT system using a copper modulator and by moving the X-ray tube position by 1.24 mm in the X and Z directions to mimic the flying focal spot. We found the low and high energy rays were well aligned, while the scatter distribution remained constant between the flying focal spot positions.

The purpose of this study is to review and compare simulation methods for describing the transport of charge clouds in silicon based semiconductor detectors and investigate the effects on energy spectrum for silicon based photon-counting strip detectors. Charge clouds and detailed carrier transport are simulated and compared using two different approaches including analytical and Monte Carlo schema. The results of the simulations are evaluated using pulse-height spectra (PHS) for a silicon strip detector with edge on geometry at two energies (25 and 75 keV) at various X-ray absorption locations relative to the pixel boundary and detector depth. The findings confirm carrier diffusion plays a large role in the charge sharing effect in photon counting detectors, in particular when the photon is absorbed near the pixel boundary far away from the pixel electrode. The results are further compared in terms of the double-counting probability for X-ray photons absorbed near the pixel boundary as a function of the threshold energy. Monte Carlo and analytical models show reasonable agreement (2% relative error in swank factor) for charge sharing effects for a silicon strip detector with edge-on geometry. For 25 keV mono-energetic photons absorbed at 5 μ m from the pixel boundary, the theoretical threshold energy at 10% double-counting probability based on charge sharing is 5.5, 8.5 and 9.2 keV for absorption depths of 50, 250 and 450 μ m from the electrode, respectively. The transport of charge clouds affects the spectral characteristics of photon counting detectors and the double-counting probability results show the theoretical threshold energy to avoid double-counting as a function of X-ray energy and X-ray interaction locations for silicon and can be considered for future studies of charge sharing effects.

Transcranial magnetic resonance-guided focused ultrasound continues to gain traction as a noninvasive treatment option for a variety of pathologies. Focusing ultrasound through the skull can be accomplished by adding a phase correction to each element of a hemispherical transducer array. The phase corrections are determined with acoustic simulations that rely on speed of sound estimates derived from CT scans. While several studies have investigated the relationship between acoustic velocity and CT Hounsfield units (HUs), these studies have largely ignored the impact of X-ray energy, reconstruction method, and reconstruction kernel on the measured HU, and therefore the estimated velocity, and none have measured the relationship directly. In this paper, 91 ex vivo human skull fragments from two skulls are imaged by 80 CT scans with a variety of energies and reconstruction methods. The average HU from each fragment is found for each scan and correlated with the speed of sound measured using a through transmission technique in that fragment. As measured by the $R$ -squared value, the results show that CT is able to account for 23%–53% of the variation in velocity in the human skull. Both the X-ray energy and the reconstruction technique significantly alter the $R$ -squared value and the linear relationship between HU and speed of sound in bone. Accounting for these variations will lead to more accurate phase corrections and more efficient transmission of acoustic energy through the skull.

Purpose Photon-counting detectors using CdTe or CZT substrates are promising candidates for future CT systems but suffer from a number of nonidealities, including charge sharing and pulse pileup. By increasing the pixel size of the detector, the system can improve charge sharing characteristics at the expense of increasing pileup. The purpose of this work is to describe these considerations in the optimization of the detector pixel pitch. Methods The transport of x rays through the CdTe substrate was simulated in a Monte Carlo fashion using GEANT4. Deposited energy was converted into charges distributed as a Gaussian function with size dependent on interaction depth to capture spreading from diffusion and Coulomb repulsion. The charges were then collected in a pixelated fashion. Pulse pileup was incorporated separately with Monte Carlo simulation. The Cramer-Rao lower bound (CRLB) of the measurement variance was numerically estimated for the basis material projections. Noise in these estimates was propagated into CT images. We simulated pixel pitches of 250, 350, and 450 microns and compared the results to a photon counting detector with pileup but otherwise ideal energy response and an ideal dual-energy system (80/140 kVp with tin filtration). The modeled CdTe thickness was 2 mm, the incident spectrum was 140 kVp and 500 mA, and the effective dead time was 67 ns. Charge summing circuitry was not modeled. We restricted our simulations to objects of uniform thickness and did not consider the potential advantage of smaller pixels at high spatial frequencies. Results At very high x-ray flux, pulse pileup dominates and small pixel sizes perform best. At low flux or for thick objects, charge sharing dominates and large pixel sizes perform best. At low flux and depending on the beam hardness, the CRLB of variance in basis material projections tasks can be 32%-55% higher with a 250 micron pixel pitch compared to a 450 micron pixel pitch. However, both are about four times worse in variance than the ideal photon counting detector. The optimal pixel size depends on a number of factors such as x-ray technique and object size. At high technique (140 kVp/500 mA), the ratio of variance for a 450 micron pixel compared to a 250 micron pixel size is 2126%, 200%, 97%, and 78% when imaging 10, 15, 20, and 25 cm of water, respectively. If 300 mg/cm2 of iodine is also added to the object, the variance ratio is 117%, 91%, 74%, and 72%, respectively. Nonspectral tasks, such as equivalent monoenergetic imaging, are less sensitive to spectral distortion. Conclusions The detector pixel size is an important design consideration in CdTe detectors. Smaller pixels allow for improved capabilities at high flux but increase charge sharing, which in turn compromises spectral performance. The optimal pixel size will depend on the specific task and on the charge shaping time.

Tools to simulate lower dose, noisy computed tomography (CT) images from existing data enable protocol optimization by quantifying the trade-off between patient dose and image quality. Many studies have developed and validated noise insertion techniques; however, most of these tools operate on proprietary projection data which can be difficult to access and can be time consuming when a large number of realizations is needed. In response, this work aims to develop and validate an image domain approach to accurately insert CT noise and simulate low dose scans. In this framework, information from the image is utilized to estimate the variance map and local noise power spectra (NPS). Normally distributed noise is filtered within small patches in the image domain using the inverse Fourier transform of the square root of the estimated local NPS to generate noise with the appropriate spatial correlation. The patches are overlapped and element-wise multiplied by the standard deviation map to produce locally varying, spatially correlated noise. The resulting noise image is scaled based on the relationship between the initial and desired dose and added to the original image. The results demonstrate excellent agreement between traditional projection domain methods and the proposed method, both for simulated and real data sets. This new framework is not intended to replace projection domain methods; rather, it fills a gap in CT noise simulation tools and is an accurate alternative when projection domain methods are not practical, for example, in large scale repeatability or detectability studies.

The x-ray source and the detector array are arguably the most critical components that determine the performance of a closed-bore CT system. This chapter reviews the historical trend and recent progress in these subsystems. This perspective can be used to predict further progress that might be made in the near future. While the basic principles of x-ray generation have not changed, there has been considerable progress in x-ray sources for CT, including the ability to withstand high forces and high power, modulate the illuminating flux, enable lower kV imaging, and maintain small focal spots at high mA. X-ray detector arrays can have a very large number of elements, allowing the development of wider cone beams. They also have lower electronic noise. The new generation of detectors will have smaller apertures and spectral resolution at the detector.

For decades, CT images were reconstructed from the measured raw data using analytical reconstruction methods, such as filtered backprojection (FBP). While FBP is fast and accurate, the measured data are rarely ideal, and iterative and statistical methods can provide significant benefit particularly when the data quality is poor. They can produce images with lower noise and can also reduce artifacts from system imperfections. However, the resulting images are nonlinear and non-stationary and have other properties that are different from those produced by FBP that should be kept in mind when the images are interpreted.

Spectral computed tomography (CT) allows optimizing image quality by combining the data in several energy channels with optimal weighting factors. In an improvement of this technique, the weighting factors are made dependent on spatial frequency, and previous work has shown that this can improve detectability for a simple detector model. In this work, we investigate the achievable detectability improvement from frequency-dependentweighting for realistic models of photon-counting detectors. We use a Monte-Carlo based simulation model to obtain point-spread functions and autocovariances for two detector models with 0.5 × 0.5 mm2 pixels, one CdTe-based with five energy bins and one silicon-based with eight energy bins. We generated noise-only images for two different energy weighting schemes: one where optimal weights were selected individually for each spatial frequency, and one where the weights optimal for zero frequency were applied to all frequencies. The modulation transfer function was set equal in both schemes. Results show that frequency-based weighting can decrease noise variance by 11 % for Si and by 38 % for CdTe, for an edge-enhancing MTF, demonstrating that optimal frequency-dependent weighting has the capability of reducing noise in high-resolution CT images.

Photon counting detectors are interesting candidates for next-generation clinical computed tomography scanners, promising improved contrast-to-noise ratio, spatial resolution and energy information compared to conventional energy-integrating detectors. Most attention is focused on cadmium telluride (CdTe) (or CZT) detectors, but silicon (Si) has been proposed as an alternative. We present detector simulation models fitted to published spectral response data for CdTe and Si, and use linear-systems theory to evaluate the spatial-frequency dependent DQE for lesion quantification and detection. Our fitted spectral response is consistent with Gaussian charge clouds with σ = 20.5 µm independent of energy for CdTe, and σ = 17 µm at 60 keV with an energy dependence of E0.54 for Si. For a silicon strip detector with 0.5 × 0.5 mm2 pixels separated by a 1D grid of 20 µm tungsten foils, the zero-frequency DQE for iodine detection is 0.43 for 30 mm detector absorption length and 0.46 for 60 mm detector absorption length. For iodine quantification in a water-iodine decomposition, the DQE is 0.26 for 30 mm and 0.27 for 60 mm Si. Compared to this detector, the DQE of a 1.6 mm thick CdTe detector with 0.225 mm pixels and two energy bins is 11-36 % higher for water and iodine detection but 28-51 % lower for material quantification. The predicted performance of Si is competitive with CdTe, suggesting that further consideration is warranted.

Purpose: Multi-detector computed tomography (MDCT) enables volumetric scans in a single breath hold and is clinically useful for hepatic imaging. For simple tasks, conventional single energy (SE) computed tomography (CT) images acquired at the optimal tube potential are known to have better quality than dual energy (DE) blended images. However, liver imaging is complex and often requires imaging of both structures containing iodinated contrast media, where atomic number differences are the primary contrast mechanism, and other structures, where density differences are the primary contrast mechanism. Hence it is conceivable that the broad spectrum used in a dual energy acquisition may be an advantage. In this work we are interested in comparing these two imaging strategies at equal-dose and more complex settings. Methods: We developed numerical anthropomorphic phantoms to mimic realistic clinical CT scans for medium size and large size patients. MDCT images based on the defined phantoms were simulated using various SE and DE protocols at pre- and post-contrast stages. For SE CT, images from 60 kVp through 140 with 10 kVp steps were considered; for DE CT, both 80/140 and 100/140 kVp scans were simulated and linearly blended at the optimal weights. To make a fair comparison, the mAs of each scan was adjusted to match the reference radiation dose (120 kVp, 200 mAs for medium size patients and 140 kVp, 400 mAs for large size patients). Contrast-to-noise ratio (CNR) of liver against other soft tissues was used to evaluate and compare the SE and DE protocols, and multiple pre- and post-contrasted liver-tissue pairs were used to define a composite CNR. To help validate the simulation results, we conducted a small clinical study. Eighty-five 120 kVp images and 81 blended 80/140 kVp images were collected and compared through both quantitative image quality analysis and an observer study. Results: In the simulation study, we found that the CNR of pre-contrast SE image mostly increased with increasing kVp while for post-contrast imaging 90 kVp or lower yielded higher CNR images, depending on the differential iodine concentration of each tissue. Similar trends were seen in DE blended CNR and those from SE protocols. In the presence of differential iodine concentration (i.e., post-contrast), the CNR curves maximize at lower kVps (80–120), with the peak shifted rightward for larger patients. The combined pre- and post-contrast composite CNR study demonstrated that an optimal SE protocol has better performance than blended DE images, and the optimal tube potential for SE scan is around 90 kVp for a medium size patients and between 90 and 120 kVp for large size patients (although low kVp imaging requires high x-ray tube power to avoid photon starvation). Also, a tin filter added to the high kVp beam is not only beneficial for material decomposition but it improves the CNR of the DE blended images as well. The dose adjusted CNR of the clinical images also showed the same trend and radiologists favored the SE scans over blended DE images. Conclusions: Our simulation showed that an optimized SE protocol produces up to 5% higher CNR for a range of clinical tasks. The clinical study also suggested 120 kVp SE scans have better image quality than blended DE images. Hence, blended DE images do not have a fundamental CNR advantage over optimized SE images.

Purpose: This paper summarizes the development of a high-power distributed x-ray source, or “multisource,” designed for inverse-geometry computed tomography (CT) applications [see B. De Man et al., “Multisource inverse-geometry CT. Part I. System concept and development,” Med. Phys. 43, 4607–4616 (2016)]. The paper presents the evolution of the source architecture, component design (anode, emitter, beam optics, control electronics, high voltage insulator), and experimental validation. Methods: Dispenser cathode emitters were chosen as electron sources. A modular design was adopted, with eight electron emitters (two rows of four emitters) per module, wherein tungsten targets were brazed onto copper anode blocks—one anode block per module. A specialized ceramic connector provided high voltage standoff capability and cooling oil flow to the anode. A matrix topology and low-noise electronic controls provided switching of the emitters. Results: Four modules (32 x-ray sources in two rows of 16) have been successfully integrated into a single vacuum vessel and operated on an inverse-geometry computed tomography system. Dispenser cathodes provided high beam current (>1000 mA) in pulse mode, and the electrostatic lenses focused the current beam to a small optical focal spot size (0.5 × 1.4 mm). Controlled emitter grid voltage allowed the beam current to be varied for each source, providing the ability to modulate beam current across the fan of the x-ray beam, denoted as a virtual bowtie filter. The custom designed controls achieved x-ray source switching in

Purpose: This paper presents an overview of multisource inverse-geometry computed tomography (IGCT) as well as the development of a gantry-based research prototype system. The development of the distributed x-ray source is covered in a companion paper [V. B. Neculaes et al., “Multisource inverse-geometry CT. Part II. X-ray source design and prototype,” Med. Phys. 43, 4617–4627 (2016)]. While progress updates of this development have been presented at conferences and in journal papers, this paper is the first comprehensive overview of the multisource inverse-geometry CT concept and prototype. The authors also provide a review of all previous IGCT related publications. Methods: The authors designed and implemented a gantry-based 32-source IGCT scanner with 22 cm field-of-view, 16 cm z-coverage, 1 s rotation time, 1.09 × 1.024 mm detector cell size, as low as 0.4 × 0.8 mm focal spot size and 80–140 kVp x-ray source voltage. The system is built using commercially available CT components and a custom made distributed x-ray source. The authors developed dedicated controls, calibrations, and reconstruction algorithms and evaluated the system performance using phantoms and small animals. Results: The authors performed IGCT system experiments and demonstrated tube current up to 125 mA with up to 32 focal spots. The authors measured a spatial resolution of 13 lp/cm at 5% cutoff. The scatter-to-primary ratio is estimated 62% for a 32 cm water phantom at 140 kVp. The authors scanned several phantoms and small animals. The initial images have relatively high noise due to the low x-ray flux levels but minimal artifacts. Conclusions: IGCT has unique benefits in terms of dose-efficiency and cone-beam artifacts, but comes with challenges in terms of scattered radiation and x-ray flux limits. To the authors’ knowledge, their prototype is the first gantry-based IGCT scanner. The authors summarized the design and implementation of the scanner and the authors presented results with phantoms and small animals.

Purpose: To find an upper bound on the maximum dose reduction possible for any reconstruction algorithm, analytic or iterative, that result from the inclusion of the data statistics. The authors do not analyzenoise reduction possible from prior knowledge or assumptions about the object. Methods: The authors examined the task of estimating the density of a circular lesion in a cross section. Raw data were simulated by forward projection of existing images and numerical phantoms. To assess an upper bound on the achievable dose reduction by any algorithm, the authors assume that both the background and the shape of the lesion are completely known. Under these conditions, the best possible estimate of the density can be determined by solving a weighted least squares problem directly in the raw data domain. Any possible reconstruction algorithm that does not use prior knowledge or make assumptions about the object, including filtered backprojection (FBP) or iterative reconstruction methods with this constraint, must be no better than this least squares solution. The authors simulated 10 000 sets of noisy data and compared the variance in density from the least squares solution with those from FBP. Density was estimated from FBP images using either averaging within a ROI, or streak-adaptive averaging with better noise performance. Results: The bound on the possible dose reduction depends on the degree to which the observer can read through the possibly streaky noise. For the described low contrastdetection task with the signal shape and background known exactly, the average dose reduction possible compared to FBP with streak-adaptive averaging was 42% and it was 64% if only the ROI average is used with FBP. The exact amount of dose reduction also depends on the background anatomy, with statistically inhomogeneous backgrounds showing greater benefits. Conclusions: The dose reductions from new, statistical reconstruction methods can be bounded. Larger dose reductions in the density estimation task studied here are only possible with the introduction of prior knowledge, which can introduce bias.

Purpose: Developing photon-counting CT detectors requires understanding the impact of parameters such as converter material, absorption length and pixel size. We apply a novel linear-systems framework, incorporating spatial and energy resolution, to study realistic silicon (Si) and cadmium telluride (CdTe) detectors at low count rate. Approach: We compared CdTe detector designs with $0.5\times0.5\; \mathrm{mm}^2$ and $0.225\times0.225\; \mathrm{mm}^2$ pixels and Si detector designs with $0.5\times0.5\; \mathrm{mm}^2$ pixels of 30 and 60 mm active absorption length, with and without tungsten scatter blockers. Monte-Carlo simulations of photon transport were used together with Gaussian charge sharing models fitted to published data. Results: For detection in a 300 mm thick object at 120 kVp, the 0.5 mm and 0.225 mm pixel CdTe systems have 28-41 $\%$ and 5-29 $\%$ higher DQE, respectively, than the 60 mm Si system with tungsten, whereas the corresponding numbers for two-material decomposition are 2 $\%$ lower to 11 $\%$ higher DQE and 31-54 $\%$ lower DQE compared to Si. We also show that combining these detectors with dual-spectrum acquisition is beneficial. Conclusions: In the low-count-rate regime, CdTe detector systems outperform the Si systems for detection tasks, while silicon outperforms one or both of the CdTe systems for material decomposition.

Purpose A dynamic bowtie filter can modulate flux along both fan and view angles for reduced patient dose, scatter, and required photon flux, which is especially important for photon counting detectors (PCDs). Among the proposed dynamic bowtie designs, the piecewise-linear attenuator (Hsieh and Pelc, Med Phys. 2013;40:031910) offers more flexibility than conventional filters, but relies on analog positioning of a limited number of wedges. In this work, we study our previously proposed dynamic attenuator design, the fluid-filled dynamic bowtie filter (FDBF) that has digital control. Specifically, we use computer simulations to study fluence modulation, reconstructed image noise, and radiation dose and to compare it to other attenuators. FDBF is an array of small channels each of which, if it can be filled with dense fluid or emptied quickly, has a binary effect on the flux. The cumulative attenuation from each channel along the x-ray path contributes to the FDBF total attenuation. Methods An algorithm is proposed for selecting which FDBF channels should be filled. Two optimization metrics are considered: minimizing the maximum-count-rate for PCDs and minimizing peak-variance for energy-integrating detectors (EIDs) at fixed radiation dose (for optimizing dose efficiency). Using simulated chest, abdomen, and shoulder data, the performance is compared with a conventional bowtie and a piecewise-linear attenuator. For minimizing peak-variance, a perfect-attenuator (hypothetical filter capable of adjusting the fluence of each ray individually) and flat-variance attenuator are also included in the comparison. Two possible fluids, solutions of zinc bromide and gadolinium chloride, were tested. Results To obtain the same SNR as routine clinical protocols, the proposed FDBF reduces the maximum-count-rate (across projection data, averaged over the test objects) of PCDs to 1.2 Mcps/mm2 , which is 55.8 and 3.3 times lower than the max-count-rate of the conventional bowtie and the piecewise-linear bowtie, respectively. (Averaged across objects for FDBF, the max-count-rate without object and FDBF is 2063.5 Mcps/mm2 , and the max-count-rate with object without FDBF is 749.8 Mcps/mm2 .) Moreover, for the peak-variance analysis, the FDBF can reduce entrance-energy-fluence (sum of energy incident on objects, used as a surrogate for dose) to 34% of the entrance-energy-fluence from the conventional filter on average while achieving the same peak noise level. Its entrance-energy-fluence reduction performance is only 7% worse than the perfect-attenuator on average and is 13% better than the piecewise-linear filter for chest and shoulder. Furthermore, the noise-map in reconstructed image domain from the FDBF is more uniform than the piecewise-linear filter, with 3 times less variation across the object. For the dose reduction task, the zinc bromide solution performed slightly poorer than stainless steel but was better than the gadolinium chloride solution. Conclusions The FDBF allows finer control over flux distribution compared to piecewise-linear and conventional bowtie filters. It can reduce the required maximum-count-rate for PCDs to a level achievable by current detector designs and offers a high dose reduction factor.

Photon-counting CT is an emerging technology with the potential to dramatically change clinical CT. Photon-counting CT uses new energy-resolving x-ray detectors, with mechanisms that differ substantially from those of conventional energy-integrating detectors. Photon-counting CT detectors count the number of incoming photons and measure photon energy. This technique results in higher contrast-to-noise ratio, improved spatial resolution, and optimized spectral imaging. Photon-counting CT can reduce radiation exposure, reconstruct images at a higher resolution, correct beam-hardening artifacts, optimize the use of contrast agents, and create opportunities for quantitative imaging relative to current CT technology. In this review, the authors will explain the technical principles of photon-counting CT in nonmathematical terms for radiologists and clinicians. Following a general overview of the current status of photon-counting CT, they will explain potential clinical applications of this technology.

Purpose Charge sharing and migration of scattered and fluorescence photons in an energy discriminating photon counting detector (PCD) degrade the detector's energy response and can cause a single incident photon to be registered as multiple events at different energies among neighboring pixels, leading to spatio-energetic correlation. Such a correlation in conventional linear, space-invariant imaging system can be usefully characterized by the frequency dependent detective quantum efficiency DQE(f). Defining and estimating DQE(f) for PCDs in a manner consistent with that of conventional detectors is complicated because the traditional definition of DQE(f) does not address spectral information. Methods We introduce the concept of presampling spectroscopic detective quantum efficiency, DQEs (f), and present an analysis of it for CdTe PCDs using a spatial domain method that starts from a previously described analytic computation of spatio-energetic crosstalk. DQEs (f) is estimated as the squared signal-to-noise ratio of the amplitude of a small-signal sinusoidal modulation of the object (cortical bone) thickness at frequency f estimated using data from the detector under consideration compared that obtained from the photon distribution incident on the detector. DQEs for material decomposition (spectral) and effective monoenergetic imaging tasks for different pixel pitch is studied based on the multipixel Cramer-Rao lower bound (CRLB) that accounts for inter pixel basis material correlation. Effective monoenergetic DQEs is estimated from the CRLB of a linear weighted combination of basis materials, and its energy dependence is also studied. Results Zero frequency DQEs for the spectral task was ~18%, 25%, and 34% for 250 μm, 500 μm, and 1 mm detector pixels respectively. Inter pixel signal correlation results in positive noise correlation between same basis material estimates of neighboring pixels, resulting in least impact on DQEs at the detector's Nyquist frequency. Effective monoenergetic DQEs (0) at the optimal energy is relatively tolerant of spectral degradation (85-91% depending on pixel size), but is highly dependent on the selected effective energy, with maximum variation (in 250 μm pixels) of 17% to 85% for effective energy between 30 to 120 keV. Conclusions Our results show that spatio-energetic correlations degrade DQEs (f) beyond what is lost by poor spectral response in a single detector element. The positive correlation between computed single basis material values in neighboring pixels results in the penalty to DQEs (f) to be the least at the Nyquist frequency of the detector. It is desirable to reduce spectral degradation and crosstalk to minimize the impact on system performance. Larger pixels sizes have better spatio-energetic response due to lower charge sharing and escape of scatter and K-fluorescence photons, and therefore higher DQEs (0). Effective monoenergetic DQEs (0) at the optimal energy is much less affected by spectral degradation and crosstalk compared to DQEs for spectral tasks.

Photon counting detectors (PCD) are widely credited with having minimum degradation from electronic noise compared to energy integrating detectors. However, they are not immune. We characterized the effect of electronic noise in simulated CdTe PCDs (0.25-1mm pixels) for spectral and effective monoenergetic tasks. Electronic noise was modeled as two separable effects - spectral blurring modeled as convolution with a Gaussian kernel with standard deviation of 7 keV, and false triggering of the lowest energy bin (depending on the threshold). To model false triggering, noise was created by filtering white Gaussian noise with a Gaussian pulse shaping kernel of 40 ns peaking time and, scaled to have a standard deviation of 7 keV, and analyzed numerically to obtain the mean and variance of false triggers at thresholds from 3 to 45 keV with ±3.5 keV hysteresis. PCDs had 5 energy bins, were operated at maximum of 20 % of characteristic count rate unless otherwise specified, and pulse pileup was not modeled. We assume the expected number of false triggers can be predicted and subtracted but that the noise from those events remains. Quantum and false triggering noise were propagated into basis material images using the Cramer-Rao Lower Bound. In basis material images, at the optimal threshold (balancing false triggers and lost true events) there was an 18-24% variance penalty compared to a detector with no electronic noise. For effective monoenergetic imaging, capturing low energy pulses performs asymptotically as well as a detector without electronic noise, with the penalty increasing with increasing energy threshold.

Synthesized monoenergetic images, generated using linear weighted combination of basis material images, portray the anatomy at a selected effective energy. Images at both high and low effective energies have been proposed as clinically useful. This paper studies the dependence of signal-to-noise ratio (SNR) and detective quantum efficiency (DQE) on the selected energy for CdTe PCDs, and for other spectral CT that uses scintillator detectors. DQE is estimated as the squared of SNR for the system being evaluated divided by that of an ideal PCD. Signal is the unbiased line integral of a material of interest and noise is estimated using propagation of the Cramer-Rao Lower Bound through the weighted sum. SNR and DQE are unimodal with the optimal energy dependent on the mean and width of the measured spectrum, on the spectral response, and system, and weakly on the material of interest. For the CdTe detectors simulated, DQE(0) at the optimal energy is relatively tolerant of spectral degradation (85-92% depending on pixel size), but is highly dependent on effective energy, with maximum variation (in 250 μm pixels) of 22-85% for effective energies between 30 to 120 keV. Study of effect of spectral distribution on DQE shows that a wider spectrum shifts the optimum to lower energy and weakens the energy dependence. In comparison to dual kV and dual layer spectral CT, PCDs have lower optimal effective energy and show higher DQE at low effective energies than energy integrating detectors with dual kV spectra.

Charge sharing and migration of scattered and fluorescence photons in photon counting detector (PCD) degrade the detector's energy response and cause a single photon to be potentially counted as multiple events in neighboring pixels, leading to correlations of signal and noise. Signal and noise correlations in conventional linear, space-invariant imaging can be usefully characterized by the frequency dependent detective quantum efficiency, DQE(f). The situation is complicated in the PCDs by the spectral dimension. We analyze DQE(f) of CdTe PCDs using a spatial domain method starting from a previously described computation of spatio-energetic cross talk. DQE(f) is estimated as the squared signal-to-noise ratio of the estimate of the amplitude of a small-signal sinusoidal modulation in the object at a frequency f by a given system compared to that with an ideal detector. DQE(f) for spectral and effective monoenergetic imaging are estimated using a multi-pixel Cramer-Rao lower bound for CdTe detectors of different pixel pitch. For a 120 kVp incident spectrum, DQE(0) for a spectral task was ~18%, 25% and 34% for 250 μm, 500 μm and 1 mm pixels, respectively. Positive correlation between same basis material estimates in neighboring pixels from the spatio-energetic cross-talk causes this effect to have least impact at the detector's Nyquist frequency. For effective monoenergetic imaging, DQE(0) at the optimal energy is relatively tolerant of spectral degradation (85-92% depending on pixel size), but is highly dependent on effective energy, with maximum variation (in 250 μm pixels) of 25-85% for effective energies between 30 to 120 keV.

In large part from concerns about radiation exposure from computed tomography (CT), iterative reconstruction (IR) has emerged as a popular technique for dose reduction. Although IR clearly reduces image noise and improves resolution, its ability to maintain or improve low-contrast detectability over (possibly post-processed) filtered backprojection (FBP) reconstructions is unclear. In this work, we have scanned a low contrast phantom encased in an acrylic oval using two vendors’ scanners at 120 kVp at three dose levels for axial and helical acquisitions with and without automatic exposure control. Using the local noise power spectra of the FBP and IR images to guide the filter design, we developed a two-dimensional angularly-dependent Gaussian filter in the frequency domain that can be optimized to minimize the root-mean-square error between the image-domain filtered FBP and IR reconstructions. The filter is extended to three-dimensions by applying a through-slice Gaussian filter in the image domain. Using this three-dimensional, non-isotropic filtering approach on data with non-uniform statistics from both scanners, we were able to process the FBP reconstructions to closely match the low-contrast performance of IR images reconstructed from the same raw data. From this, we conclude that most or all of the benefits of noise reduction and low-contrast performance of advanced reconstruction can be achieved with adaptive linear filtering of FBP reconstructions in the image domain.

A dynamic bowtie filter can modulate flux along both fan and view angles for reduced dose, scatter, and required detector dynamic range. Reducing the dynamic range requirement is crucial for photon counting detectors. One approach, the piecewise-linear attenuator (Hsieh and Pelc, Med Phys 2013), has shown promising results both in simulations and an initial prototype. Multiple wedges, each covering a different range of fan angle, are moved in the axial direction to change their attenuating thickness as seen in an axial slice. We report on an implementation of a filter with precision components and a control algorithm targeted for operation on a table-top system. Algorithms for optimizing wedge position and mA modulation and for correcting bowtie-specific beam-hardening artifacts are proposed. In experiments, the error between expected and observed bowtie transmission was ~2% on average and ~7% at maximum for a chest phantom. Within object boundaries, the observed flux dynamic ranges of 42, for a chest phantom, and 25, for an abdomen phantom were achieved, corresponding to a reduction factor of 5 and 11 from the object scans without the bowtie. With beam hardening correction, the mean CT number in soft tissue regions was improved by 79 HU on average, and deviated by 7 HU on average from clinical scanner CT images. The implemented piecewise-linear attenuator is able to dynamically adjust its thickness with high precision to achieve flexible flux control.

The development of energy-resolving photon-counting detectors for medical x-ray imaging is attracting considerable attention. Since the image quality can be degraded by different nonidealities such as charge sharing, Compton scatter and fluorescence, there is a need for developing performance metrics in order to compare and optimize detector designs. For conventional, non-energy-resolving detectors, this is commonly done using the linear-systems-theory framework, in which the detector performance is described by noise-equivalent quanta (NEQ) and detective quantum efficiency (DQE) as functions of spatial frequency. However, these metrics do not take the energy-resolving capabilities of multibin photon-counting detectors into account. In this work, we present a unified mathematical framework for quantifying the performance of energy-resolving detectors. We show that the NEQ and DQE can be generalized into matrix-valued quantities, which describe the detector performance for detection tasks with both spatial and energy dependence. With this framework, a small number of simple measurements or simulations are sufficient to compute the dose efficiency of a detector design for any imaging task, taking the effects of detector nonidealities on spatial and energy resolution into account. We further demonstrate that the same framework also can be used for assessing material quantification performance, thereby extending the commonly used performance metrics based on the Cramer-Rao lower bound to spatial-frequency-dependent tasks. The usefulness of the proposed framework is demonstrated using simulations of charge sharing and fluorescence in a CdTe detector.

Photon-counting energy resolving detectors are subject to intense research interest, and there is a need for a general framework for performance assessment of these detectors. The commonly used linear-systems theory framework, which measures detector performance in terms of noise-equivalent quanta (NEQ) and detective quantum efficiency (DQE) is widely used for characterizing conventional X-ray detectors but does not take energy-resolving capabilities into account. We extend this framework to encompass energy-resolving photon-counting detectors and elucidate how the imperfect energy response of real-world detectors affects imaging performance. We generalize NEQ and DQE to matrix-valued quantities as functions of spatial frequency, and show how these can be calculated from simple Monte Carlo simulations. To demonstrate how the new metrics can be interpreted, we compute them for simplified models of fluorescence and Compton scatter in a photon-counting detector and for a Monte Carlo model of a CdTe detector with 0.5 x 0.5 mm^2 pixels. Our results show that the ideal-linear-observer performance for any detection or material quantification task can be calculated from the proposed metrics. Off-diagonal elements in these matrices are shown to be related to imperfect energy resolution. The Monte Carlo model of the CdTe detector predicts a zero-frequency dose efficiency relative to an ideal detector of 0.86 and 0.65 for detecting water and bone, respectively. When the task instead is to quantify these materials, the corresponding values are 0.34 for water and 0.26 for bone. We have shown that the matrix-valued NEQ and DQE metrics contain sufficient information for calculating the dose efficiency for both detection or quantification tasks, the task having any spatial and energy dependence. This framework will be beneficial for the development of photon-counting X-ray detectors., The final version was published in Medical Physics Correction made in proof: Just before Eq. 20, "an ideal detector" should be "a detector that is purely photon-counting (i.e. does not measure photon energy) but ideal in all other respects"